Question

The escape velocity at the surface of Earth is approximately 11 km/s. What is the mass, in units of ME (the mass of the Earth), of a planet with three times the radius of Earth for which the escape speed is three times that for Earth?

Answer 1

Answer:11 km/s

Step-by-step explanation:

Given

Escape velocity at the surface of earth is 11 km/s

Escape velocity is given by

`V_e=\sqrt{(2GM)/(R)}`

Escape velocity at the surface of earth

`11=\sqrt{(2GM)/(R)}`--------------------1

If Escape velocity is three times and the radius is also the three times

`V_e_2=\sqrt{(2G(3M))/(3R)}`

`V_e_2=\sqrt{(2GM)/(R)}=V_e`

i.e.
`V_e_2=11 km/s`